Problem: ${\sqrt[3]{640} = \text{?}}$
Solution: $\sqrt[3]{640}$ is the number that, when multiplied by itself three times, equals $640$ First break down $640$ into its prime factorization and look for factors that appear three times. So the prime factorization of $640$ is $2\times 2\times 2\times 2\times 2\times 2\times 2\times 5$ Notice that we can rearrange the factors like so: $640 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 = (2\times 2\times 2) \times (2\times 2\times 2) \times 2\times 5$ So $\sqrt[3]{640} = \sqrt[3]{2\times 2\times 2} \times \sqrt[3]{2\times 2\times 2} \times \sqrt[3]{2\times 5}$ $\sqrt[3]{640} = 2\times 2 \times \sqrt[3]{2\times 5}$ $\sqrt[3]{640} = 4 \sqrt[3]{10}$